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# If ab = b, which of the following must be true?

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Manager
Joined: 28 Jun 2018
Posts: 125
Location: India
Concentration: Finance, Marketing
GPA: 4
If ab = b, which of the following must be true?  [#permalink]

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27 Aug 2018, 01:11
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Difficulty:

35% (medium)

Question Stats:

55% (01:00) correct 45% (00:39) wrong based on 31 sessions

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If ab = b, which of the following must be true?

A) a=1
B) b=0
C) a=1 and b=0
D) a=1 or b=1
E) a=1 or b=0

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Joined: 02 Aug 2009
Posts: 6786
Re: If ab = b, which of the following must be true?  [#permalink]

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27 Aug 2018, 01:16
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GMATbuster92 wrote:
if ab=b , which of the following must be true?
A) a=1
B) b=0
C) a=1 and b=0
D) a=1 or b=1
E) a=1 or b=0

$$ab=b........ab-b=0........b(a-1)=0$$
so a=1 or b=0 or both

E
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Re: If ab = b, which of the following must be true?  [#permalink]

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27 Aug 2018, 01:20
fairly straightforward:

ab=b

any number multiplied by 1 remains the same:
1.b=b
--> a=1
there is no other option for a to be anything else since that would modify the outcome

then ask yourself: is there an option where b on it's own can make this true:
the only case where any variable number of times a number = that number is for 0
1.b=b
2.b=b
3.b=b
is only ever true for b=0

since we figured out these 2 requirements a=1, b=0 separately, this means there is no dependency, hence:
OR

a=1 or b=0

--> E

kudos if this helped
Re: If ab = b, which of the following must be true? &nbs [#permalink] 27 Aug 2018, 01:20
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